How would you go about estimating populations of dolphins?
Get further into power series using the fascinating Bessel's equation.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Which pdfs match the curves?
Which line graph, equations and physical processes go together?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Explore the properties of matrix transformations with these 10 stimulating questions.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Use vectors and matrices to explore the symmetries of crystals.
Who will be the first investor to pay off their debt?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.
Why MUST these statistical statements probably be at least a little bit wrong?
Explore the relationship between resistance and temperature
How do you choose your planting levels to minimise the total loss at harvest time?
Which of these infinitely deep vessels will eventually full up?
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you find the volumes of the mathematical vessels?
Get some practice using big and small numbers in chemistry.
Invent scenarios which would give rise to these probability density functions.
Work out the numerical values for these physical quantities.
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Go on a vector walk and determine which points on the walk are closest to the origin.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the shape of a square after it is transformed by the action of a matrix.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Match the descriptions of physical processes to these differential equations.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
This problem explores the biology behind Rudolph's glowing red nose.
Are these estimates of physical quantities accurate?
When you change the units, do the numbers get bigger or smaller?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Match the charts of these functions to the charts of their integrals.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Which dilutions can you make using only 10ml pipettes?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Explore the properties of perspective drawing.
Which units would you choose best to fit these situations?
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.